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You are here: Home  »  CAT Questions  »  Quant, Math  »  Permutation Combination »  Rearranging Letters

Permutation : Rearranging Letters of a Word

Question 5

In how many ways can the letters of the word ABACUS be rearranged such that the vowels always appear together?

(1) 6!/2!

(2) 3!*3!

(3) 4!/2!
(4) 4!*3!/2!

(5) 72

Correct Answer is 4!*3!/2! - Choice 4

Explanation

ABACUS is a 6 letter word with 3 of the letters being vowels.

If the 3 vowels have to appear together as stated in the question, then there will 3 consonants and a set of 3 vowels grouped together.

One group of 3 vowels and 3 consonants are essentially 4 elements to be rearranged.

The number of possible rearrangements is 4!

The group of 3 vowels contains two 'a's and one 'u'.

The 3 vowels can rearrange amongst themselves in 3!/2! ways as the vowel "a" appears twice.

Hence, the total number of rearrangements in which the vowels appear together are 4!3!/2






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